Comparative study of projection schemes for stochastic finite element analysis

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Assessment of spectral representation and Karhunen–Loève expansion methods for the simulation of Gaussian stochastic fields (2007, methodology): “[1,2,5,7,8,15,33,45].”
A reduced spectral function approach for the stochastic finite element analysis (2011, methodology): “These methods include the polynomial chaos (PC) expansion [5], stochastic reduced basis method [28–30] and Wiener–Askey chaos expansion [10–12].”
Global sensitivity analysis using polynomial chaos expansions (2008, methodology): “…work by (Ghanem and Spanos, 1991) has been applied to many engineering problems (see a review by Sudret and Der Kiureghian (2000) and many recent papers, among others Le Maˆıtre et al. (2001); Keese and Matthies (2005); Sudret et al. (2004); Sudret et al. (2006); Sachdeva et al. (2006a,b)).”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, background): “Let us mention and give some comments on the Stochastic Reduced Basis Method [86, 87, 111, 112], proposed for solving a class of linear stochastic problems.”
The stochastic finite element method: Past, present and future (2009, methodology): “As a result, SRBMs are computationally efficient with regard to PCE at a comparable level of accuracy and are thus suitable for solving large-scale linear problems (for an exhaustive comparison of these projection schemes see [154]), as can be seen in Fig.”